Also, Vision and computer Game AI will be very different fields of study. The former will most probably end up relying on difficult statistics (not every computer scientists cup of tea) whereas computer games usually end up being about heuristics, logic and prehaps human factors. Also you should consider how crowded each field is and whether you think you can make an impact.

As a self funded phd student, your supervisor might not care or give up on you. The supervisor risks nothing in loosing you if he is already famous and doesnt have to worry about research council funding. I was at cambridge and know many stories of people effectively being abandoned. It is also full of academic tourists who are attracted for the name.

Inexperienced supervisrors can be very crap. But they can be more commited and are likely to be supervising a project close to their core expertise rather than "branching out" projects

I am currently a student in London and the opportunities and activities are awesome looking across the breadth of colleges. University of London degrees have a very good reputation.